The discovery of superconductivity (SC) with a transition temperature, Tc, up to 65K in single-layer FeSe (bulk Tc =8K) films grown on SrTiO3 substrates has attracted special attention to Fe-based thin films. The high Tc is a consequence of the combined effect of electron transfer from the oxygen-vacant substrate to the FeSe thin film and lattice tensile strain. Here we demonstrate the realization of SC in the parent compound BaFe2As2 (no bulk Tc) just by tensile lattice strain without charge doping. We investigate the interplay between strain and SC in epitaxial BaFe2As2 thin films on Fe-buffered MgAl2O4 single crystalline substrates. The strong interfacial bonding between Fe and the FeAs sublattice increases the Fe-Fe distance due to the lattice misfit which leads to a suppression of the antiferromagnetic spin density wave and induces SC with bulk-Tc ?10K. These results highlight the role of structural changes in controlling the phase diagram of Fe-based superconductors.